Problem: Simplify the following expression: $ y = \dfrac{8}{p - 6} - \dfrac{7}{6} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{6}{6}$ $ \dfrac{8}{p - 6} \times \dfrac{6}{6} = \dfrac{48}{6p - 36} $ Multiply the second expression by $\dfrac{p - 6}{p - 6}$ $ \dfrac{7}{6} \times \dfrac{p - 6}{p - 6} = \dfrac{7p - 42}{6p - 36} $ Therefore $ y = \dfrac{48}{6p - 36} - \dfrac{7p - 42}{6p - 36} $ Now the expressions have the same denominator we can simply subtract the numerators: $y = \dfrac{48 - (7p - 42) }{6p - 36} $ Distribute the negative sign: $y = \dfrac{48 - 7p + 42}{6p - 36}$ $y = \dfrac{-7p + 90}{6p - 36}$